INDUCTIVE INFERENCE OF OPTIMAL PROGRAMS A SURVEY AND OPEN PROBLEMS

The present paper surveys results and presents open problems concerning the limiting-effective synthesis of optimal programs for recursive functions given by input-output examples. Five different formalizations of the intuitive notion ''optimal program'' are given. In particular, it is studied under what conditions the knowledge that every function from a function class does possess an ''optimal program'' is sufficient to infer such an ''optimal program'' in the limit for each function contained in the class.